Given a wire and a piece of foil wired to a bread board, is it possible using capacitors wired in series (or some other method) to significantly reduce the capacitance of the wire/foil?
I'm not 100% sure I understand your needs, but you might consider a negative capacitance amplifier, as in http://en.wikipedia.org/wiki/Negative_impedance_converter, whose parallel negative input impedance should subtract that of your wire. This is a positive feedback trick, so if your negative capacitance is too high, your system will go unstable.
This is used all the time in neuroscience to deal with large capacitances in glass microelectrodes, but I've never seen it used for cable capacitance.
I've used double screened cable. The inner core signal is applied to a unity gain amplifier which projects back the same voltage onto the 1st (inner screen). This means that the inner core "sees" a capacitance that is vastly reduced. The outer screen is used as ground and of course the inner screen "sees" all the ground capacitance.
I've used this on a capacitance probe too.
Things that make it go wrong - long wires where the frequency used has a wavelength that approaches (maybe) 100th of the cable length. Significant attenuation down the cable (losses) means it isn't as effective.
Use high impedance inputs on your actual cap-probe input and the non-inverting screen driver input.